This activity is designed to follow the activities From Secant Lines to Tangent Lines and Slopes and Derivatives [referenced below], but it can easily stand on its own. Using a dynamic tangent line and the value of the tangent line's slope, students analyze the graph of a function, investigating relationships between the function's first derivative, absolute and local extrema, intervals of increasing and decreasing, concavity, and inflection points. As the lesson progresses, students create and refine a sketch of f '(x).

This material is based upon work supported by the
National Science Foundation under Grant DUE-0226284.
Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the
National Science Foundation.